Answer
(a) See explanations.
(b) $6898$
Work Step by Step
(a) Step 1. The starting fish population is $P_0=5000$,
Step 2. At the end of the first month, the population will in crease by $8\%$ which gives $1.08P_0$, then reduces by $300$ due to harvesting which gives the end population for this month as $P_1=1.08P_0-300$ ,
Step 3. Similarly, at the end of the second month, the population will be $P_2=1.08P_1-300$ ... ...
Step 4. Repeat the process for $n-$months to get $P_n=1.08P_{n-1}-300$.
(b) After 12 month, the population will be about $6898$ as shown in the figure where calculations have been performed for up to 12 months.
